Question: $\dfrac{3}{8} \div \dfrac{5}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{5}{9}$ is $\dfrac{9}{5}$. Therefore: $ \dfrac{3}{8} \div \dfrac{5}{9} = \dfrac{3}{8} \times \dfrac{9}{5} $ $ \phantom{\dfrac{3}{8} \times \dfrac{9}{5}} = \dfrac{3 \times 9}{8 \times 5} $ $ \phantom{\dfrac{3}{8} \times \dfrac{9}{5}} = \dfrac{27}{40} $